DYNAMICS OF A POINT. 



III. Constrained Motion on Curves or Surfaces: 

 Particles joined by Strings. 



1406. A particle is constrained to move on a curve under the 

 action of forces, sucli that if projected from a certain point of the 



with velocity v, it would describe the curve freely. Prove 

 that, when projected from that point with velocity T, the pressure 



V s v* 

 on the curve is always m , p being the radius of curvature 



at any point, and m the mass of the particle, 



1407. A particle is acted on by two forces, one parallel to a 

 straight line and constant, and the other tending from a 



fixed point and varying as (dist.)"*, and the particle is initially at 

 rest at a point where these forces are equal; prove that it will 

 proceed to describe a parabola whose focus is the fixed p >int and 

 axis parallel to the fixed line. 



T\vo particles A t B are together in a smooth circular 

 : A attracts B with a force whose acceleration is ft . di>' 

 nnd ni'.vrs al-ii:; tli" tube with uniform angular velocity 2 v //x; 

 nitially at n-st ; prove that the angle <f> subtended at the 

 re by AB after a time t is given by the equation 



1 100. A particle i placed in a sin Uolic groove whieh 



own plane about the fi>eu< with uniform angular 



., and th< describes in .-paee an e.jual confocal 



]ir:ibol;i, nnd'T an at t 1 a< -t :\ < f-Ter in the foCUS ; pr.-\e t'iat this 



force at any point is measured by 



ng the focal distance and LV th-- latus rectum. 



